Here’s an example to back up your statement:
On my Mom’s side, both of her parents came from Italy. My grandfather became a US citizen before my Mom was born (in the USA), my Grandmother was not a US citizen at the time.
Italy will not grant my Mom citizenship because her father was a US citizen when she was born. They could care less that her mother wasn’t a US citizen (which she became later); it’s all about the Father.
I have literal first hand knowledge. I was born in Boston to an American citizen father and a Canadian citizen mother. I am not a natural born citizen. I cannot become president. I had a US Customs officer and a professor of law at Northeastern University tell me that 30 years ago.
And this has what to do with U.S. constitution and U.S. citizenship? The U.S. does not care what Italy or any other country does. It does not affect U.S. law. Think about it.